On a certain criterion of the existence of generalized derivative from Orlicz Class

• Autorzy: Borsuk M.
• Języki publikacji: EN

Abstrakty

EN

In terms of difference quotients it is established the existence of generalized derivative of the function.

Słowa kluczowe

EN

difference quotient; generalized derivative; Orlicz classes

PL

funkcja rzeczywista; iloraz różnicowy; klasa Orlicza; pochodna uogólniona

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 1998
• Tom: Vol. 46, no. 2
• Strony: 173--178
• Opis fizyczny: Bibliogr. 8 poz.,

Twórcy

autor

Borsuk M.

• Department of Applied Mathematics, Agriculture and Technical University, Oczapowskiego 1, 10-957 Olsztyn-Kortowo, Poland

Bibliografia

• [1] S.М. Nikol`sky, Approximation of functions of several variables and embedding theorems (in Russian), Nauka, Moscow 1969.
• [2] M. A. Krasnoselsky, Ja. B. Rutitsky, Convex functions and Orlicz spaces, (in Russian), Nauka, Moscow 1958.
• [3] J. P. Nаtanson, The theory of functions of a real, variable (in Russian), Nauka, Pvloscow 1974.
• [4] N. Dunford, J. Т. Schwartz, Linear operators. Part I: General theory, Int. Pub., 1958.
• [5] C. Va1ee- Poussin, Sur l'integrale de Lebesgue, Trans. Amer. Math. Soc.,
• 16 (1915) 451-452.
• [6] E. M. Stein, Singular integrals and differentiability properties of functions, Princeton Univ. Press, Princeton 1970.
• [7] О. V. Besov, V. P. Il'in, S. M. Nikol'ky, Integrad representations of functions and embedding theorems (in Russian), Nauka, Moscow 1975.
• [8] Review J. Math., (in Russian), Moscow, 2В (1974) 688 Dep.